How to create UV and texture for egg shaped model
Try to reproject your texture upon a catmull-clark subdivided version of the mesh with the subdivide UVs option disabled.

This way you should be able to have more faces (and so a higher projecting accuracy), while maintaining the same UV islands.

Before:



After:



In my testfile this process was able to mitigate the effect of the distortion.

Once reprojected the texture, you can obiuvsly delete the modifier and keep your vertex count untouched.